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To solve the simultaneous equations \( y + x = 2 \) and \( 2y - 3x = 9 \) using the graph provided:

1. The green line represents the equation \( y + x = 2 \), or \( y = 2 - x \).
2. The yellow line represents the equation \( 2y - 3x = 9 \), or \( y = \frac{3x + 9}{2} \).

From the graph, we need to find the point where these two lines intersect, as that will give the solution to the system of equations.

By observing the intersection of the two lines, we can see that they meet at the point \( (-3, 5) \). Therefore:

\[
x = -3, \quad y = 5
\]

The solution to the simultaneous equations is:

\[
x = -3, \quad y = 5
\]

Would you like to explore more details about how these equations were graphed or why this method works?

Here are 5 related questions to deepen your understanding:
1. How do we solve simultaneous equations algebraically?
2. What is the meaning of the slope in each of these equations?
3. How do you convert an equation to slope-intercept form from standard form?
4. Can simultaneous equations have no solution or infinite solutions?
5. What are other methods to solve simultaneous equations besides graphing?

**Tip**: Always double-check your intersection point by substituting the values back into the original equations.

From the graph, determine the solution to the simultaneous equations y + x = 2 and 2y - 3x = 9. What are the values of x and y?

Learn how to solve the simultaneous equations y + x = 2 and 2y - 3x = 9 by using a graph. This example shows how to find the point of intersection for two linear equations and the solution to the system. Ideal for students in Grades 8-10.

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